Puzzling out leading-0 edge cases was interesting.

Cool concept, tests are annoying though.
I don't like that certain simplifications are required,
such as tan(x)' equaling 1 + tan^2(x) rather than sec^2(x).
Also (* x x) is rejected because of (^ x 2).

More nitpicky:
f(x)^g(x) => (g'(x)ln(f(x))+g(x)f'(x)/f(x))(f(x)^g(x)) is the general form (which works for monomials as well)
but I needed to hardcode in the specific monomial form to pass some tests.

That may be an interesting problem on its own:
Check if two functions that only use: constants 'x' + - * / ^ cos sin tan exp ln
are equal.
Though idk if that's even possible/decidable.